Bilateral filter with data model

ABSTRACT

A method of filtering a target pixel in an image forms, for a kernel of pixels comprising the target pixel and its neighbouring pixels, a data model to model pixel values within the kernel; calculates a weight for each pixel of the kernel comprising: (i) a geometric term dependent on a difference in position between that pixel and the target pixel; and (ii) a data term dependent on a difference between a pixel value of that pixel and its predicted pixel value according to the data model; and uses the calculated weights to form a filtered pixel value for the target pixel, e.g. by updating the data model with a weighted regression analysis technique using the calculated weights for the pixels of the kernel; and evaluating the updated data model at the target pixel position so as to form the filtered pixel value for the target pixel.

BACKGROUND

The present disclosure relates to a method of filtering a target pixelin an image.

Image filters are often used to process images. For example, an imagefilter may be used to blur or sharpen an image. One example of an imagefilter is a bilateral filter.

A bilateral filter is a non-linear, edge-preserving, and noise-reducingsmoothing filter for images. A standard bilateral filter can determine afiltered value (I_(filtered)(x)) for a target pixel based on a weightedaverage of intensity values from neighbouring pixels. For example, aweighted sum of neighbouring pixel values (I(x_(i))) within a kernel (Ω)can be used, wherein the weight for a particular neighbouring pixel inthe sum is based on both: (i) the spatial distance between the targetpixel and the neighbouring pixel (∥x_(i)−x∥), and (ii) the differencebetween the target pixel value and the neighbouring pixel value(∥I(x_(i))−I(x)∥). The kernel (Ω) would typically be a square kernel(e.g. 3×3 or 5×5) centred on the target pixel (x), but in general thekernel could be any suitable shape and size.

For example, a filtered pixel value, I_(filtered)(x), at position x maybe given as:

${I_{filtered}(x)} = {\frac{1}{K}{\sum\limits_{x_{i} \in \Omega}\;{{I\left( x_{i} \right)}{d\left( {{I\left( x_{i} \right)} - {I(x)}} \right)}{g\left( {x_{i} - x} \right)}}}}$where d is a data term, often referred to as the “photometric costfunction”, which is a function of the difference between the targetpixel value and the neighbouring pixel value (I(x_(i))−I(x)) and g is ageometric term which is a function of the spatial distance between thetarget pixel and the neighbouring pixel (x_(i)−x); and K is anormalisation term, given by K=Σ_(x) _(i)_(∈Ω)d(I(x_(i))−I(x))g(x_(i)−x).

The data term (d) and the geometric term (g) can, for example, beGaussian functions, for example:

${d(q)} = {{e^{- \frac{{q}^{2}}{2\sigma_{d}^{2}}}\mspace{14mu}{and}\mspace{14mu}{g(q)}} = e^{- \frac{{q}^{2}}{2\sigma_{g}^{2}}}}$where σ_(d) and σ_(g) are smoothing parameters.

When the argument q is set to the pixel value difference I(x_(i))−I(x)the data term (d) becomes:

$d = e^{- \frac{{{{I{(x_{i})}} - {I{(x)}}}}^{2}}{2\sigma_{d}^{2}}}$

And similarly, when the argument q is set to the spatial distancex_(i)−x the geometric term (g) becomes:

${g = e^{- \frac{{{x_{i} - x}}^{2}}{2\sigma_{g}^{2}}}}\mspace{14mu}$

The functions d( ) and g( ) are both Gaussian functions, differing onlyin the smoothing parameters σ_(d) and σ_(g).

However, standard bilateral filters often produce a flattened output,yielding an “oil-painting” effect, whereby subtle gradients areflattened and false edges are introduced into filtered images.

SUMMARY

This summary is provided to introduce a selection of concepts that arefurther described below in the detailed description. This summary is notintended to identify key features or essential features of the claimedsubject matter, nor is it intended to be used to limit the scope of theclaimed subject matter.

According to a first aspect of the present invention there is provided amethod of filtering a target pixel in an image comprising: forming, fora kernel of pixels comprising the target pixel and its neighbouringpixels, a data model to model pixel values within the kernel;calculating a weight for each pixel of the kernel comprising: (i) ageometric term dependent on a difference in position between that pixeland the target pixel; and (ii) a data term dependent on a differencebetween a pixel value of that pixel and its predicted pixel valueaccording to the data model; and using the calculated weights for thepixels in the kernel to form a filtered pixel value for the targetpixel.

Using the calculated weights may comprise: updating the data model witha weighted regression analysis technique using the calculated weightsfor the pixels of the kernel; and evaluating the updated data model atthe target pixel position so as to form the filtered pixel value for thetarget pixel.

The method may further comprise performing one or more iterations of thecalculating and updating steps, wherein updated weights are calculatedusing the updated data model of the preceding iteration.

Updating the data model may comprise minimising a weighted sum of thesquared residual errors between the pixel values of the kernel predictedby the data model and the corresponding actual pixel values of thekernel.

The weighted regression analysis technique may comprise performing aweighted least squares method.

The weighted regression analysis technique may comprise performing aweighted local gradient measurements method.

Forming a data model may comprise applying a first filter to the kernelso as to form a target pixel value for use in calculating the weights.

The first filter may be a bilateral filter.

The data model may be defined by one or more parameters including one ormore gradient parameters, β, and an estimated value, Î, at the positionof the target pixel, and wherein forming the data model comprisesselecting a data model defining a curve or surface suitable formodelling the pixel values within the kernel, and setting the one ormore gradient parameters of the data model to zero.

The data model may be a bilinear data model, a linear data model, abiquadratic data model, a quadratic data model, a parametric data modelor a polynomial data model.

Each pixel value may comprise one or more characteristics of therespective pixel.

Each characteristic may be one or more of depth information, informationdescribing normal vectors for surfaces identified in the image, textureinformation, luma, luminance, chrominance, brightness, lightness, hue,saturation, chroma, colourfulness, or any colour component.

The method may further comprise forming the filtered pixel value for thetarget pixel for a first channel in accordance with any preceding claim;and forming a second filtered pixel value for the target pixel for asecond channel in dependence on a second data model, by: forming, forthe kernel of pixels comprising the target pixel and its neighbouringpixels, a second data model to model a second characteristic representedby pixel values within the kernel; calculating a weight for each pixelof the kernel comprising: (i) a geometric term dependent on a differencein position between that pixel and the target pixel; and (ii) a dataterm dependent on a difference between a pixel value of that pixel andits predicted pixel value according to the second data model; and usingthe calculated weights for the pixels in the kernel so as to form asecond filtered pixel value for the target pixel.

The kernel may be symmetric about the target pixel.

The kernel may be asymmetric about the target pixel.

The filtering may be cross filtering, such that the filtered pixel valueis in a first channel, and the data term is dependent on pixel valuedifferences in a second channel.

The data term may be dependent on pixel value differences in more thanone channel.

Forming a data model may comprise: determining average gradients (β) inboth x and y directions, from a summation of multiple pixel valuedifferences determined from pairs of pixels located within the kernel;determining, from each pixel in the kernel, an estimated pixel value Îat the target pixel position based on the determined average gradients;determining a model pixel value Î at the target pixel position byperforming a weighted sum of the estimated pixel values Î determinedfrom each of the pixels in the kernel.

According to a second aspect of the present invention there is provideda data processing system for filtering a target pixel in an image, thedata processing system comprising: a data model formation unitconfigured to form, for a kernel of pixels comprising the target pixeland its neighbouring pixels, a data model to model pixel values withinthe kernel; a weight calculating unit configured to calculate a weightfor each pixel of the kernel comprising: (i) a geometric term dependenton a difference in position between that pixel and the target pixel; and(ii) a data term dependent on a difference between a pixel value of thatpixel and its predicted pixel value according to the data model; a datamodelling unit configured to use the calculated weights for the pixelsin the kernel so as to form a filtered pixel value for the target pixel.

The data modelling unit may comprise: a data model updating unitconfigured to update the data model with a weighted regression analysistechnique using the calculated weights for the pixels of the kernel; anda data model evaluating unit configured to evaluate the updated datamodel at the target pixel position so as to form a filtered pixel valuefor the target pixel.

The data processing system may be configured to perform one or moreiterations of the calculating in the weight calculating unit and theupdating in the data model updating unit, wherein the weight calculatingunit is configured to use the updated data model of the precedingiteration to calculate updated weights.

The data model updating unit may be configured to update the data modelby minimising a weighted sum of the squared residual errors between thepixel values of the kernel predicted by the data model and thecorresponding actual pixel values of the kernel.

The data model may be defined by one or more parameters including one ormore gradient parameters, β, and an estimated value, Î, at the positionof the target pixel, and wherein the data model formation unit isconfigured to select a data model defining a curve or surface suitablefor modelling the pixel values within the kernel, and set the one ormore gradient parameters of the data model to zero.

There is also provided a data processing system configured to performthe method described herein. The data processing system may be embodiedin hardware on an integrated circuit. There may be provided a method ofmanufacturing, at an integrated circuit manufacturing system, the dataprocessing system. There may be provided an integrated circuitdefinition dataset that, when processed in an integrated circuitmanufacturing system, configures the system to manufacture the dataprocessing system. There may be provided a non-transitory computerreadable storage medium having stored thereon a computer readabledescription of an integrated circuit that, when processed in anintegrated circuit manufacturing system, causes the integrated circuitmanufacturing system to manufacture the data processing system.

There may also be provided an integrated circuit manufacturing systemcomprising: a non-transitory computer readable storage medium havingstored thereon a computer readable integrated circuit description thatdescribes the data processing system; a layout processing systemconfigured to process the integrated circuit description so as togenerate a circuit layout description of an integrated circuit embodyingthe data processing system; and an integrated circuit generation systemconfigured to manufacture the data processing system according to thecircuit layout description.

There may be provided computer program code for performing a method asdescribed herein. There may be provided non-transitory computer readablestorage medium having stored thereon computer readable instructionsthat, when executed at a computer system, cause the computer system toperform the methods as described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

The present invention is described by way of example with reference tothe accompanying drawings. In the drawings:

FIG. 1 depicts a system for filtering an image.

FIG. 2 schematically depicts a data model for a kernel of five pixels.

FIG. 3 is a flow diagram illustrating an exemplary iterativeimplementation of a system for filtering an image.

FIG. 4 depicts an exemplary image filtering system.

FIG. 5a depicts an input image.

FIG. 5b depicts a result of filtering the input image of FIG. 5a using astandard bilateral filter.

FIG. 5c depicts a result of filtering the input image of FIG. 5a usingthe system for filtering an image described herein.

FIG. 6 is a schematic diagram of an integrated circuit manufacturingsystem.

DETAILED DESCRIPTION

The following description is presented by way of example to enable aperson skilled in the art to make and use the invention. The presentinvention is not limited to the examples described herein and variousmodifications to the disclosed embodiments will be apparent to thoseskilled in the art. Embodiments are described by way of example only.

The examples described herein relate to bilateral filters, however, theymay be applicable to other image filters.

Standard bilateral filters often “flatten” subtle gradients andintroduce false edges into filtered images. One reason that this occursis because the data term (d) tends to bias pixel values towards beingthe same as the neighbouring pixel values. That is, the data term (d)makes a larger contribution to the weighted combination when aneighbouring pixel has a similar value to the target pixel. In otherwords, the data term (d) assumes that pixels relevant to the targetpixel have similar value. However, regions of uniform pixel value thatsatisfy this assumption are very rare in most real images. That is,there is usually at least some gradient across the pixel values presentin real-images.

An alternative method for filtering a target pixel value is providedherein. A data model can be formed for modelling the variation in thepixel values of an image. The data model can be fitted to the pixelvalues of the image using a weighted linear regression technique. Theweights applied to the pixel values of the image during fitting arebased on the weights traditionally defined by the bilateral filterequation. That is, the weights may comprise a data term and a geometricterm as presented above, but in contrast to traditional bilateralfilters the data term is additionally dependent on the data modelitself. The updated data model can be evaluated at the target pixelposition so as to provide a filtered value for the target pixel. Theweights, the data model and the filtered value for the target pixel arehence interdependent, and may be iteratively refined.

Image filters in accordance with the present disclosure provide goodmodelling and good denoising for soft gradients in images, and few or noflattening artefacts are produced. An example is shown in FIGS. 5a to 5c. FIG. 5a depicts an input image; FIG. 5b depicts a result of filteringthe input image of FIG. 5a using a standard bilateral filter; and FIG.5c depicts a result of filtering the input image of FIG. 5a using thesystem for filtering an image described herein. It can be seen in FIG.5b that the standard bilateral filter flattens subtle gradients, whichproduces the slightly mottled (“oil-painting”) effect into the image;whereas the image in FIG. 5c is smoother over the section having slightgradients, whilst still preserving the edges.

FIG. 1 depicts a system 101 for filtering an image. The system 101 maycomprise a data model formation unit 102, a weight calculating unit 103,and a data modelling unit 107. The data modelling unit 107 may comprisea data model updating unit 104, and a model evaluating unit 105. Thesystem may also comprise an iterative loop 106.

An image is input to the system. The image may be, for example, a stillimage or a frame of a video. The image may comprise a plurality ofpixels. The input may represent all of the pixels of an image, or asub-set of the pixels of an image. The output of the system may be oneor more filtered pixels of the image. All of, or a sub-set of, thepixels of the input may be filtered and output from the system.

Data Model

In accordance with the following examples, a data model may be formed bydata model formation unit 102 to model the pixel values within a kernel.The data model may be suitable for modelling the pixel values, within akernel, of the image input into the system. For example, the data modelmay be a first-order, or a higher order, data model of the pixel valueswithin the kernel.

The data model may be used to model the variation in pixel values withinone or more kernels. Each kernel may include a target pixel to befiltered and a plurality of neighbouring pixels. The data model maymodel the local gradients surrounding the target pixel. A kernel (11)may be any suitable size and/or shape. Typically, the kernel may be asquare kernel (e.g. 3×3 or 5×5 pixels) centred on the target pixel (x).For denoising applications, a kernel of 9×9 pixels centred on the targetpixel (x) may be considered to be suitable. In some examples, the kernelmay be asymmetric. It is also possible that the kernel may not becentred on the target pixel.

The data model may be used to model the variation in one or more valuesassociated with the pixels in a kernel. Each pixel value may compriseone or more characteristics of the respective pixel. For example, thecharacteristics indicated by the pixel values may include luma,luminance, chrominance, brightness, lightness, hue, saturation, chroma,colourfulness, or any colour component, such as Red, Green or Bluecolour components. For example, the data model may model the variationin the luminance (Y) values associated with the pixels. In otherexamples, the data model may model the variation in chrominance (UV), orany one or more of red (R), green (G) or blue (B) components, luma,luminance, chrominance, brightness, lightness, hue, saturation, chroma,colourfulness, or any colour component. It may also be possible to modelthe variation in other pixel values, such as pixel values indicated indepth maps, normal maps or albedo maps (surface texture) associated withthe image. In some examples, it may be possible to generate multiplemodels, each model modelling the variation in pixel values for adifferent characteristic.

The data model may be formed by selecting, in data model formation unit102, a model representing a curve or a surface. The curve or surface maybe of any arbitrary order. In a preferred example, the data model is abilinear model. A bilinear model is a function of two variables that areindependently linear in both those variables. A bilinear model can modelthe variation in pixel values in both the ‘x’ and ‘y’ directions. Thus,bilinear models are particularly suitable for use in the filtering oftwo-dimensional images. In one example, a bilinear model may be:β(x _(i) −x)+Î

Where β represents a 2D gradient and is represented as a vector, i.e.β=[β_(x), β_(y)], and Î is an estimated value at the position of thetarget pixel value (x). In this example, the bilinear data modelrepresents a plane, where points on the plane can be expressed as thesum of: (i) an estimated value at the target pixel position, x and (ii)the result of a vector multiplication (a dot product) of the 2D gradientβ with a difference in position (x_(i)−x) between a neighbouring pixelto be weighted and the target pixel. In some examples, the target pixelmay be defined to be at an origin of a coordinate system for the filterkernel (i.e. at x=[0,0]), such that the data model can be expressed moresimply as βx_(i)+Î.

Data Term

The formed data model may be incorporated into a data term. The dataterm in accordance with the examples defined herein may be based on thedata term as traditionally defined in the bilateral filter equation. Asbriefly described above, this modified data term and a geometric termmay be used in fitting the data model to the pixels within the kernel.The data model may enable the data term to account for variation betweenneighbouring pixels that typically exists in real images.

In an example, the data term used in filtering a target pixel value inaccordance with the examples given herein may be:d(I(x _(i))−β(x _(i) −x)−Î)where I(x_(i)) is the neighbouring pixel value at position x_(i), and Îis a current or running estimate for the target pixel value.

In situations where the filter is only to be used in a non-iterativemanner, or for a first iteration of the filter comprising an iterativeloop 106, the current or running estimate for the target pixel value maybe the value of the target pixel as input to the system, I(x). For thesecond and subsequent iterations, the current or running estimate forthe target pixel value may be the value for the target pixel valueestimated in the previous iteration.

The data model may represent a predicted value for each pixel of thekernel of pixels of the image. That is, the value of the data model at aposition, x_(i), may represent a predicted value for a pixel at thatposition within a kernel.

For example, FIG. 2 schematically depicts a data model 207 generated fora kernel of five pixels 202, 203, 204, 205 and 206. The kernel comprisestwo pixels positioned either side of the target pixel 202. The datamodel 207 may be a bilinear data model, where the variation in pixelvalues by position in only one dimension (e.g. x or y) is depicted inFIG. 2. The data model 207 models the variation in the pixel values ofpixels 202, 203, 204, 205 and 206 within the kernel. Schematically, apredicted pixel value for each of the neighbouring pixel positions inthe kernel could be read from the data model 207.

By incorporating a data model into the data term, the weight for eachneighbouring pixel may be dependent on the difference between the actualvalue of each neighbouring pixel and the value predicted for that pixelaccording to the data model. In this way, the weight for eachneighbouring pixel in the filtering process may be increased if thatneighbouring pixel has a value which is closer to the value predicted bythe model.

For example, referring back to FIG. 2, pixels 203 and 204 have the samepixel value. For the data term of a standard bilateral filter (without adata model) the value of the data term for each of these pixels 203, 204would be the same. However, by incorporating a data model in the dataterm in accordance with present disclosure, the data term for pixel 204would be greater than the data term for pixel 203. This is because thevalue of pixel 204 is closer than the value of pixel 203 to the valuepredicted by the data model 207. Considering now pixels 205 and 206,pixel 205 has the same value as the target pixel 202, whereas pixel 206has a very different pixel value to the target pixel 202. Because ofthis, for the data term of a standard bilateral filter (without a datamodel) the data term for pixel 205 would be greater than the data termfor pixel 206. However, according to the examples given herein, the dataterm for pixel 206 may be greater than the data term for pixel 205because pixel 206 is closer than the value of pixel 205 to the valuepredicted by the data model 207.

Filtering

As described below, the current or running estimate for the target pixelvalue (Î) may be directly derivable from the data model. That is, it maynot be necessary to perform a full weighted combination of pixel valuesas in a traditional bilateral filter.

In some examples, the parameters of the formed data model, e.g. β and Î,may initially be set such that β=[0,0] and Î=I(x). In some examples, thecoefficients of the data model may be estimated in dependence on priorknowledge of the input pixel values.

Prior to evaluating the formed data model, the data model may be updatedby the data model updating unit 104. Updating the data model, i.e.updating the parameters β_(x), β_(y) and Î may involve fitting the datamodel to the values of the pixels in the kernel. Fitting the model mayinvolve minimising the error between the data model and the values ofthe pixels within the kernel, e.g. using an unweighted linear leastsquares technique, although in examples described in detail herein aweighted linear least squares technique is used. Fitting the model mayresult in the coefficients or parameters of the data model, e.g. β_(x),β_(y) and Î being updated.

In some examples, in a first iteration, the data model may be fit to thepixel values of the kernel as input to the system. In other examples,prior to the first iteration, an initial standard filtering step isperformed (e.g. in accordance with the standard bilateral filterequation).

The fitting of the data model may be performed by a weighted regressionanalysis technique. A weighted regression analysis technique may be anytechnique in the art that can be used to fit a model to a data set, inwhich the values of the data set are weighted. For example, the fittingof the data model may be performed using a weighted linear least squaresmethod, a weighted local gradients measurement method, or any othersuitable weighted regression analysis technique. Fitting a model using aweighted local gradient measurement method may involve measuring thepixel value gradients within a kernel by measuring the differencesbetween pairs of pixel values, weighted according to data and geometricterms, as described below. Weighted local gradient measurements maytherefore represent the variation in pixel values about a target pixel.

Thus, in order to update the data model, the weights for the weightedregression analysis must be calculated. This step may be performed bythe weight calculating unit 103. The weight calculating unit 103 maycalculate weights based on the weights traditionally used in a bilinearfilter weighted combination. That is, the weight for a particularneighbouring pixel in the weighted regression analysis is based on both(i) a data term that, according to examples given herein, incorporates adata model, and (ii) a geometric term based on a difference in positionbetween the neighbouring pixel and the target pixel. The weights used toupdate the data model may take the form:W(x _(i) ,x)=d(I(x _(i))−β(x _(i) −x)−Î)g(x _(i) −x)

Where d( ) and g( ) are Gaussian functions as described above, theexpanded expression for the weights becomes:

${W\left( {x_{i},x} \right)} = {e^{- \frac{{{{I{(x_{i})}} - {\beta{({x_{i} - x})}} - \hat{I}}}^{2}}{2\sigma_{d}^{2}}}e^{- \frac{{{x_{i} - x}}^{2}}{2\sigma_{g}^{2}}}}$where σ_(d) and σ_(g) are the smoothing parameters. The smoothingparameters may be based on an estimate of the level of noise in animage, with larger values typically being chosen to provide moresmoothing in images or parts of images with higher levels of noise.

In this example the functions d( ) and g( ) are both Gaussian functions.The Gaussian has an appropriate peaked shape and is easily calculated,but alternative functions may also be used. For example, a triangularfunction, or a function defined by a spline, e.g. a cubic spline, may beused instead. The functions used for d( ) and g( ) do not need to be ofthe same type. For example, d( ) may use a Gaussian while g( ) uses atriangular function.

Thus, updating the data model may comprise minimising a weighted sum ofthe squared residual errors between the pixel values for theneighbouring pixels predicted by the data model and the correspondingactual neighbouring pixel values of the kernel. In other words, the datamodel may be updated by finding the values of β_(x), β_(y) and Îaccording to:

$\min\limits_{\beta,\hat{I}}{\sum\limits_{i \in \Omega}\;{{W\left( {x_{i},x} \right)}{{{I\left( x_{i} \right)} - {\beta\left( {x_{i} - x} \right)} - \hat{I}}}^{2}}}$

Once the data model has been updated, the value of the data model at thetarget pixel position, x (e.g. I(0) in the case where the target pixelis at the centre of the kernel) can be evaluated and thus the current orrunning estimate for the target pixel value, Î, can be updated.

The process of: (1) calculating weights in dependence on the data modelparameters β_(x), β_(y) and Î; (2) updating the data model using aweighted linear regression technique such as a weighted linear leastsquares technique; and (3) evaluating the model so as to determine theupdated data model parameters β_(x), β_(y) and Î: may be repeatediteratively.

That is, if a further iteration is to be performed the model parameters(β_(x), β_(y) and Î) are also evaluated by the data model evaluatingunit 105 for feeding back into the weight calculating unit 103. Theupdated the model parameters (β_(x), β_(y) and Î) may be fed back intothe weight calculating unit via iterative loop 106. The filter weightsmay therefore change between iterations because they depend on the modelparameters (β_(x), β_(y) and Î) of the previous iteration.

FIG. 3 is a flow diagram illustrating an exemplary iterative use of asystem for filtering an image configured in accordance with theprinciples described herein.

In step 301, a data model for representing the variation in pixel valueswithin the kernel is formed in accordance with the examples describedabove.

In step 302, a set of weights are calculated based on a geometric termand a data term which includes the data model as described in theexamples given herein.

In step 303, the data model is updated using a weighted linearregression technique (e.g. a weighted linear least squares technique) independence on the calculated weights.

In step 304, the updated data model is evaluated so as to determine theupdated data model parameters β_(x), β_(y) and Î.

If, at decision 305, no further iterations are to be performed, thecurrent or running estimate for the target pixel value, Î, may be output306 as the filtered target pixel value.

If, at decision 305, further iterations are to be performed, the updateddata model parameters (β_(x), β_(y) and Î) are used to re-calculate theweights in step 302. The process of updating 303 and evaluating 304 thedata model can be repeated. In this way, the current estimate of thetarget pixel value, Î (as well as the other data model parameters (β_(x)and β_(y)) can be iteratively refined.

The number of iterations to be performed may be dependent on thecomputational resources available. In other examples, the type of pixelvalue being filtered, or the order of the data model being used, may bea factor in deciding how many iterations are to be performed. The numberof iterations to be performed may also be determined dynamically, e.g.in dependence on a weighted measure of error between the valuespredicted for the pixels within the kernel by the data model and thevalues of the pixels in the kernel. For example, the method could stopiterating when the weighted sum of squared errors (Σ_(i∈Ω)W(x_(i),x)∥I(x_(i))−β(x_(i)−x)−Î ∥²) is below a threshold.

The filtering process may be repeated for each of the pixels in theinput image, or for a subset of the pixels in the input image. Forexample, only a section of an image may be filtered. In other examples,every other pixel may be filtered. The filtering process minimises thenoise in an image, because each of the output filtered target pixelvalues is dependent on a number of neighbouring pixel values. In thatway, outlying pixel values may be removed.

Exemplary Filtering Algorithm

The iterative filtering of a target pixel value according to the presentdisclosure may be performed according to the following exemplaryalgorithm. In this example the data model is a bilinear model.

Inputs:

I(x), x∈Ω—the current working kernel, with the target/output pixel atx=0.

g(x)—A geometric cost function.

d (I(x)—βx—Î)—A photometric cost function dependent on a data model, βxand an estimate of the target pixel value, Î, where β is a vector havingcomponents β_(x) and β₃, (i.e. β=[β_(x), β_(y)]) defining the gradientof the bilinear model in x and y directions.

σ_(g)—Geometric smoothing parameter.

σ_(d)—Data smoothing parameter.

N_(iter)—the number of fitting iterations to perform.

Output:

Î— a new estimate for the value at the target/output pixel location x=0.

Algorithm:

-   -   1. Initialise gradient parameters: β←[0 0].    -   2. Initialise target pixel estimate: Î←I(0).    -   3. For i=1 . . . N_(iter) (repeat N_(iter) times)        -   a. Compute weights: W(x)←g(x)d(I(x)−βx−Î)        -   b. Estimate β, Î using weighted linear least squares applied            to the pixel values I(x) in the kernel Ω, using the weights            W(x).            where the parameters, β and Î, of the bilinear data model            may be found using weighted linear least squares as follows:

The coordinates of all the pixels in the kernel may be arranged in anM×3 matrix,

${X = \begin{bmatrix}x_{1} & \ldots & x_{M} \\1 & \ldots & 1\end{bmatrix}^{T}},$where M is the number of pixels in the kernel Ω. The pixel values may bearranged in a column vector,i=[I(x ₁) . . . I(x _(M))]^(T).

The data model may be expressed as,i=X[β_(x)β_(y) Î]^(T).

The standard weighted linear least squares solution to this equation is,[β_(x)β_(y) Î]^(T)=(X ^(T) WX)⁻¹ X ^(T) Wi

Here W is a diagonal matrix containing the weights computed inaccordance with the present disclosure,W _(j,j) =W(x _(j))=g(x)d(I(x)−βx−Î)

Alternative Non-Iterative Method

In the examples given above, an iterative method solves simultaneouslyfor the weights and the data model, including the filtered pixel valueÎ, where the weights and data model depend on each other.

In an alternative example, a data model may be determined first, usingany appropriate fitting method. The filter may then be applied to thekernel using a weighted combination, with weights determined withrespect to the data model.

For example, a data model may be found using a method such as one basedon local gradient measurement. Such a method may determine averagegradients (β) in both x and y directions, from a summation of multiplepixel value differences determined from pairs of pixels located withinthe kernel. Weighting may be applied to the pixel value differences, forexample based on a photometric cost function, but without the use of adata model.

Similarly, a value for Î may be found, which may be a weighted orunweighted average of the pixel values within the kernel, and which mayalso be based on the determined average gradients. For example, eachpixel value at position x_(i) within the kernel may be used to providean estimate for Î at the target pixel position x based on the determinedgradients and the difference in position between the target pixelposition x and the position x_(i). For example, an estimate for Î usingthe pixel value at position x_(i) may be given by I(x_(i))−β(x₁−x). Theestimates for Î from the different pixel values within the kernel canthen be summed and normalised, e.g. using a weighted sum, to determine amodel pixel value Î at the target pixel position. The weights of theweighted sum may be determined as described above, e.g. based on aphotometric cost function.

Finally, an output pixel value may be determined by computing weights,according to the determined data model, and applying those weights in aweighted sum:

W(x) ← g(x)  d(I(x) − β x − Î)$I_{filtered} = {\frac{1}{K}{\sum\limits_{x \in \Omega}\;{{I(x)}{W(x)}}}}$where K is the normalisation term:

$K = {\sum\limits_{x \in \Omega}\;{W(x)}}$

Alternative Data Models

In the examples described above, the data model is a bilinear model.However, various data models may be incorporated into the data term of abilateral filter. For example, the models may be linear, bilinear,biquadratic, parametric, polynomial models of any arbitrary order, orany other suitable model.

In an example, a simple linear model may be appropriate. For example, asimple linear model may take the form, α(x_(i)−x), where α=[α_(x)]).Images may be filtered using linear kernels, i.e. 1D kernels. Forexample, an image may be filtered by filtering each of the rows orcolumns of pixels using one or more linear kernels. Alternatively, therows of pixels in an image may first be filtered using linear kernels,followed by the filtering of the columns of pixels using linear kernels,or vice versa.

In another example, a biquadratic model may be incorporated into thedata term. For example, the data term may take the form:d(I(x _(i))−(x _(i) −x)^(T) A(x _(i) −x)−β(x _(i) −x)−Î)

In this example, A is a 2×2 second order gradient coefficient matrix.

It can be advantageous to use higher order models (i.e. higher orderthan linear/bilinear models) which can provide more accurate models ofimage values within kernels of pixels within the image. For example,where the kernel is relatively large, it may become apparent that thecurvature of the data is not approximated sufficiently well by thelinear/bilinear model over the width of the kernel. That is,conceptually, if you were to look at a section of data representing acurve through a small enough kernel, each small section of that curvemay appear as a straight line. In this case, using a bilinear model maybe suitable for modelling each small section of the curve. However, ifyou were to look at the same data through a larger kernel it may becomeclear that a curve is present. In this case, a higher order model may bedesirable to accurately account for the curvature. However, typicallyhigher order models have a greater computational cost, and there can bedifficulties due to degenerate cases (e.g. cases where there is notenough data to uniquely and stably determine the model). In addition,poor higher order models can result in over-fitting which may enhancenoise features instead of removing them.

In some examples, the data model may not be of the same order in both‘x’ and ‘y’ directions. For example, the model could be linear in the‘x’ direction and quadratic in the ‘y’ direction. With reference to thebiquadratic data model described above, this could be achieved bysetting one or more of the coefficients in A, a 2×2 second ordergradient matrix, to zero. For example, video sequences comprising asequence of 2D image frames have two spatial dimensions and one temporaldimension. Data in the temporal dimension may be filtered using adifferent model to data in the spatial dimensions.

The type or order of the model chosen may be dependent on the type ofpixel values being modelled (e.g. luminance, chrominance etc.). Forexample, if the filter were to be used to filter luminance (Y) values, ahigher order model, e.g. a first-order (i.e. bilinear) model may besuitable. When filtering chrominance values, a lower order model, e.g. azeroth-order (i.e. constant) model may be more suitable. This choice maybe made in dependence on prior knowledge of the resilience of a type ofpixel value to over-fitting. In other cases, this choice may be madebased on trial and error.

Cross Filters

Where pixel values have multiple channels (e.g. RGB channels or YUVchannels), the filter may be implemented as a cross filter (or “jointfilter”). In a cross filter example, the data term may be dependent ondifferences in more than one channel.

For example, in YUV images, the luminance (Y) channel tends to have moreresolution and detail than the chrominance (U and V) channels. A dataterm based on the content of the Y channel may therefore be used whenfiltering the chrominance channels to identify image features (e.g.edges) that are not apparent in the chrominance data alone. In othercases, the chrominance channels may have features that are not apparentin the luminance channel. The data term used in calculating weights maybe a function of data terms from some or all of the channels, e.g. amaximum or average value of data terms.

In other examples, non-image data may be available. For example, animage may be taken by a camera that incorporates a depth sensor, suchthat a depth value is available for each image pixel, indicating thedistance from the camera of the object visible at that pixel. Changes indepth value may indicate image features, e.g. edges that are notapparent from the image data alone, and may therefore provide usefulinformation that can be incorporated into a data term. Depth dataproduced by a camera is often noisy and may require pre-processingbefore being used in this way. In some examples, image data may be usedin a cross filter to condition depth data, and depth data may be used ina cross filter to condition image data.

Another application of a cross filter configured in accordance with theprinciples herein may be in denoising ray-traced images, whereadditional information can be produced by the renderer, e.g. depth maps,normal maps, albedo maps (surface texture), etc. In this example theadditional maps are of high quality and can support higher order modelswithout experiencing problems with over-fitting to noise.

Asymmetric Kernels

According to the examples described herein, the filter may useasymmetric kernels (kernels with fewer pixels on one side of the centrepixel than on the other, or greater weight assigned on one side of thecentre pixel) without introducing asymmetric artefacts into the filteredoutput.

When using an asymmetric kernel, the classic bilateral filter produces aresult that is effectively translated/shifted towards the centre of thekernel.

When a linear or higher order data model is introduced into the dataterm in accordance with the present disclosure, this problem does notoccur to the same extent. The data models described herein arefitted/updated so as to represent the variation in pixel values across akernel. The embodiments of the invention described herein work toproduce a filtered value by evaluating a data model. The data model isfitted to the data in the entire kernel according to the data andgeometry terms defined herein. Therefore a filtered output value may beproduced at any position within the kernel by evaluating the model atthat position. Although the result will still reflect the weightings ofthe bilateral filter so that pixels with higher weights have a greaterinfluence on the filtered pixel value, the gradient terms add anextrapolation effect so that the output estimate remains at the intendedcoordinates.

Example Implementations

In the following we present exemplary implementations of the system andmethod for filtering of a target pixel in an image as disclosed herein.These exemplary implementations may be performed using a system forfiltering an image as described herein, in accordance with FIG. 1.

Example 2

FIG. 4 depicts an exemplary image filtering system. The image filteringsystem of FIG. 4 may comprise a cross or joint bilateral filter (407).The data model may be a bilinear model with respect to luminance. Theimage filtering system of FIG. 4 may be particularly applicable as adenoising filter.

In Example 2, an image may be input from RGB window (401) in RGB colourspace. Noise estimator (405) may use the target pixel to estimate thelocal noise variance. The noise estimate may be converted to chrominancecolour space by noise colour converter (406). The target pixel value mayby filtered by the joint bilateral filter with bilinear luminance model(407). The target pixel estimate may be initialised with the inputtarget pixel value and the luminance gradients may initially be set to0. At each iteration, the error between the estimate and the inputwindow may be measured and used to calculate data weights. A new modelestimate may be computed using the input window and weights. The finalpixel estimate may be converted back to RGB space by pixel colourconvert (418). Example 2 may be performed according to the followingalgorithms for (a) a denoising filter, (b) a photometric costcomputation, and (c) model fitting:

(a) Denoising Filter

Input:

I_(RGB) The RGB image.

σ_(LUT)—Noise curve look-up tables.

k_(σ)—Noise variance scale factor.

(w, h)—The kernel/window size.

N_(JBL) The number of iterations of the joint bilateral filter process.

Output:

Î_(RGB) A new estimate of the RGB image.

Algorithm:

-   -   1. At each target pixel, p_(RGB), the RGB noise estimates,        {σ_(R) ², σ_(G) ², σ_(B) ²}, may be obtained from the noise        curve look-up tables and scaled by k_(σ).    -   2. The RGB noise estimates may be converted to YUV space noise        estimates to give σ_(n) ²={σ_(Y) ², σ_(U) ², σ_(V) ²}.    -   3. A local RGB window may be converted to YUV, to produce a w×h        window of pixels, Ω(x, y), with the target pixel aligned with        Ω(0,0).    -   4. The target pixel estimate, {circumflex over (p)}_(YUV), may        be initialised as the target pixel in the input local YUV        window, {circumflex over (p)}_(YUV)←Ω(0,0).    -   5. The bilinear luminance gradient parameters may be initialised        to zero, g_(x)←0, g_(y)←0.    -   6. The following may be repeated N_(JBL) times to improve the        YUV pixel estimate:        -   a) Compute photometric costs C_(p) and geometric costs            C_(G).            -   Where C_(p) is calculated as below, and C_(G)=g(x)        -   b) Generate weights using photometric and geometric costs:            W=C_(p). C_(G).        -   c) Update pixel and gradient estimates using model fitting.    -   7. The final target pixel estimate may be converted back to RGB        space to yield {circumflex over (p)}_(RGB).

(b) Photometric Cost Computation

Photometric cost computation may be performed by photometric costcomputation unit (409).

Input:

{circumflex over (p)}_(YUV)={{circumflex over (p)}_(Y), {circumflex over(p)}_(U), {circumflex over (p)}_(V)}—The current target pixel estimatein YUV space.

{g_(x), g_(y)}—The current bilinear luminance gradient parameters.

σ_(n) ²={σ_(Y) ², σ_(U) ², σ_(V) ²}—The pixel noise estimate in YUVspace.

Ω(x, y)={Y(x, y), U(x, y), V(x, y)—The local window of YUV space pixels,where coordinates (0,0) are aligned with the target pixel.

Output:

C_(p)(x, y)—The photometric costs window corresponding to Ω(x, y).

Algorithm:

The pixel error for each pixel in the window may be computed as,

$\begin{matrix}{{{e\left( {x,y} \right)} = {\begin{bmatrix}{Y\left( {x,y} \right)} \\{U\left( {x,y} \right)} \\{V\left( {x,y} \right)}\end{bmatrix} - \begin{bmatrix}{{\hat{p}}_{Y} + {xg}_{x} + {yg}_{y}} \\{\hat{p}}_{U} \\{\hat{p}}_{V}\end{bmatrix}}},} \\{= {\begin{bmatrix}{e_{Y}\left( {x,y} \right)} & {e_{U}\left( {x,y} \right)} & {e_{V}\left( {x,y} \right)}\end{bmatrix}^{\bigwedge}{T.}}}\end{matrix}$

The photometric cost may be calculated from the joint, noisevariance-normalised error,C _(p)(x,y)=d(e _(Y)(x,y),σ_(Y))·d(w _(c) e _(U)(x,y),σ_(U))·d(w _(c) e_(V)(x,y),σ_(V))where the function for the data term d( ) is modified to take anadditional argument for the smoothing parameter σ:

${{d\left( {q,\sigma} \right)} = e^{- \frac{{q}^{2}}{2\sigma^{2}}}}\mspace{11mu}$and tuneable parameter, w_(c), is a weight that may be applied to thechrominance components to control their relative importance compared tothe luminance component.

(c) Model Fitting

Model fitting may be performed by model fitting unit (412).

The model fitting process may estimate new pixel value and luminancegradient values from the kernel window and weights.

Inputs:

Ω(x, y)={Y(x, y), U(x, y), V(x, y)—The local window of YUV space pixels,where coordinates (0,0) are aligned with the target pixel.

W (x, y)—The kernel weights corresponding to Ω(x, y).

Output:

{circumflex over (p)}_(YUV)={{circumflex over (p)}_(Y), {circumflex over(p)}_(U), {circumflex over (p)}_(V)}—A new target pixel estimate in YUVspace.

{g_(x), g_(y)}—A new set of bilinear luminance gradient parameters.

Algorithm:

The following moments of the weights may be used in computations below:

${\mu_{0} = {{\mu_{0}(W)} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}\;{W\left( {x,y} \right)}}}},{\mu_{x} = {{\mu_{x}(W)} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}\;{x\;{W\left( {x,y} \right)}}}}},{\mu_{y} = {{\mu_{y}(W)} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}\;{y\;{W\left( {x,y} \right)}}}}},{\mu_{xx} = {{\mu_{xx}(W)} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}\;{x^{2}\;{W\left( {x,y} \right)}}}}},{\mu_{xy} = {{\mu_{xy}(W)} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}\;{{xy}\;{W\left( {x,y} \right)}}}}},{\mu_{yy} = {{\mu_{yy}(W)} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}\;{y^{2}\;{{W\left( {x,y} \right)}.}}}}}$

The chrominance channels may be modelled using a zero order model, whichis fitted using simple weighted averaging:

${{\hat{p}}_{U} = {\mu_{0}^{- 1}{\sum\limits_{\forall{{({x,y})} \in \Omega}}{{W\left( {x,y} \right)}{U\left( {x,y} \right)}}}}},{{\hat{p}}_{V} = {\mu_{0}^{- 1}{\sum\limits_{\forall{{({x,y})} \in \Omega}}{{W\left( {x,y} \right)}{{V\left( {x,y} \right)}.}}}}}$

The luminance channel may be modelled using a bilinear model, definedas:Ŷ(x,y)={circumflex over (p)} _(Y) +xg _(x) +yg _(y)

The bilinear model may be fitted to the data using the method ofWeighted Linear Least Squares (WLLS). The WLLS algorithm has beenreformulated as a set of weighted sums, to avoid matrix inversions. Itmay be possible for the data to be in a degenerate configuration, sothat it is not possible to resolve all three parameters of the modeluniquely. There may be two degenerate configurations:

-   -   1. Only one pixel has non-zero weight. In this case {circumflex        over (p)}_(Y) may be equal to the pixel with non-zero weight        (usually the target pixel, so that {circumflex over (p)}_(Y) is        unchanged), and g_(x)=g_(y)=0. This case may be detected by        checking for μ_(xx)=μ_(yy)=0.    -   2. Pixels with non-zero weight may be arranged in a straight        line, so that only one gradient is defined. This 1D degeneracy        may be detected by checking if the second order moments form a        singular matrix.

There may therefore be three cases that each require a solution, aslisted below.

Non-Degenerate Case:

$\mspace{79mu}{{d = {{\mu_{xx}\left( {{\mu_{yy}\mu_{0}} - \mu_{y}^{2}} \right)} + {\mu_{xy}\left( {{\mu_{x}\mu_{y}} - {\mu_{xy}\mu_{0}}} \right)} + {\mu_{x}\left( {{\mu_{xy}\mu_{y}} - {\mu_{x}\mu_{yy}}} \right)}}},{g_{x} = {d^{- 1}{\sum\limits_{\forall{{({x,y})} \in \Omega}}\;{\left( {{\left( {{\mu_{yy}\mu_{0}} - \mu_{y}^{2}} \right)x} + {\left( {{\mu_{x}\mu_{y}} - {\mu_{xy}\mu_{0}}} \right)y} + \left( {{\mu_{xy}\mu_{y}} - {\mu_{x}\mu_{yy}}} \right)} \right){W\left( {x,y} \right)}{Y\left( {x,y} \right)}}}}},{g_{y} = {d^{- 1}{\sum\limits_{\forall{{({x,y})} \in \Omega}}\;{\left( {{\left( {{\mu_{x}\mu_{y}} - {\mu_{xy}\mu_{0}}} \right)x} + {\left( {{\mu_{xx}\mu_{0}} - \mu_{x}^{2}} \right)y} + \left( {{\mu_{xy}\mu_{x}} - {\mu_{xx}\mu_{y}}} \right)} \right){W\left( {x,y} \right)}{Y\left( {x,y} \right)}}}}},{{\hat{p}}_{Y} = {d^{- 1}{\sum\limits_{\forall{{({x,y})} \in \Omega}}\;{\left( {{\left( {{\mu_{xy}\mu_{y}} - {\mu_{x}\mu_{yy}}} \right)x} + {\left( {{\mu_{xy}\mu_{x}} - {\mu_{xx}\mu_{y}}} \right)y} + {\mu_{xx}\mu_{yy}} - \mu_{xy}^{2}} \right){W\left( {x,y} \right)}{{Y\left( {x,y} \right)}.}}}}}}$

In the 1D degenerate case, only one gradient may be defined. Instead ofdefining a new 1D coordinate system, it may be desirable to use theexisting coordinate system. The non-zero pixels may be aligned witheither x- or y-axis, or may be at some other angle. The solution is asfollows:

${d_{x} = {{\mu_{xx}\mu_{0}} - \mu_{x}^{2}}},{d_{y} = {{\mu_{yy}\mu_{0}} - \mu_{y}^{2}}},{g_{x}^{\prime} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}{\left( {{\mu_{0}x} - \mu_{x}} \right){W\left( {x,y} \right)}{Y\left( {x,y} \right)}}}},{g_{y}^{\prime} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}{\left( {{\mu_{0}y} - \mu_{y}} \right){W\left( {x,y} \right)}{Y\left( {x,y} \right)}}}},{{\hat{Y}}_{x} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}{\left( {\mu_{xx} - {\mu_{x}x}} \right){W\left( {x,y} \right)}{Y\left( {x,y} \right)}}}},{{\hat{Y}}_{y} = {\sum\limits_{\forall{{({x,y})} \in \Omega}}{\left( {\mu_{yy} - {\mu_{y}y}} \right){W\left( {x,y} \right)}{{Y\left( {x,y} \right)}.}}}}$

If μ_(xx)≥μ_(yy)

-   -   d=d_(x),    -   g_(x)=d⁻¹g_(x)′,    -   g_(y)=0    -   {circumflex over (p)}_(Y)=d⁻¹Ŷ_(x),        else    -   d=d_(y),    -   g_(x)=0    -   g_(y)=d⁻¹g_(y)′,    -   {circumflex over (p)}_(Y)=d⁻¹Ŷ_(y).

In the point degenerate case: {circumflex over (p)}_(Y) is unchanged.

The data processing system of FIGS. 1 and 4 are shown as comprising anumber of functional blocks. This is schematic only and is not intendedto define a strict division between different logic elements of suchentities. Each functional block may be provided in any suitable manner.It is to be understood that intermediate values described herein asbeing formed by a data processing system need not be physicallygenerated by the data processing system at any point and may merelyrepresent logical values which conveniently describe the processingperformed by the data processing system between its input and output.

The data processing systems described herein may be embodied in hardwareon an integrated circuit. The data processing system s described hereinmay be configured to perform any of the methods described herein.Generally, any of the functions, methods, techniques or componentsdescribed above can be implemented in software, firmware, hardware(e.g., fixed logic circuitry), or any combination thereof. The terms“module,” “functionality,” “component”, “element”, “unit”, “block” and“logic” may be used herein to generally represent software, firmware,hardware, or any combination thereof. In the case of a softwareimplementation, the module, functionality, component, element, unit,block or logic represents program code that performs the specified taskswhen executed on a processor. The algorithms and methods describedherein could be performed by one or more processors executing code thatcauses the processor(s) to perform the algorithms/methods. Examples of acomputer-readable storage medium include a random-access memory (RAM),read-only memory (ROM), an optical disc, flash memory, hard disk memory,and other memory devices that may use magnetic, optical, and othertechniques to store instructions or other data and that can be accessedby a machine.

The terms computer program code and computer readable instructions asused herein refer to any kind of executable code for processors,including code expressed in a machine language, an interpreted languageor a scripting language. Executable code includes binary code, machinecode, bytecode, code defining an integrated circuit (such as a hardwaredescription language or netlist), and code expressed in a programminglanguage code such as C, Java or OpenCL. Executable code may be, forexample, any kind of software, firmware, script, module or librarywhich, when suitably executed, processed, interpreted, compiled,executed at a virtual machine or other software environment, cause aprocessor of the computer system at which the executable code issupported to perform the tasks specified by the code.

A processor, computer, or computer system may be any kind of device,machine or dedicated circuit, or collection or portion thereof, withprocessing capability such that it can execute instructions. A processormay be any kind of general purpose or dedicated processor, such as aCPU, GPU, System-on-chip, state machine, media processor, anapplication-specific integrated circuit (ASIC), a programmable logicarray, a field-programmable gate array (FPGA), or the like. A computeror computer system may comprise one or more processors.

It is also intended to encompass software which defines a configurationof hardware as described herein, such as HDL (hardware descriptionlanguage) software, as is used for designing integrated circuits, or forconfiguring programmable chips, to carry out desired functions. That is,there may be provided a computer readable storage medium having encodedthereon computer readable program code in the form of an integratedcircuit definition dataset that when processed in an integrated circuitmanufacturing system configures the system to manufacture a dataprocessing system configured to perform any of the methods describedherein, or to manufacture a data processing system comprising anyapparatus described herein. An integrated circuit definition dataset maybe, for example, an integrated circuit description.

There may be provided a method of manufacturing, at an integratedcircuit manufacturing system, a data processing system as describedherein. There may be provided an integrated circuit definition datasetthat, when processed in an integrated circuit manufacturing system,causes the method of manufacturing a data processing system to beperformed.

An integrated circuit definition dataset may be in the form of computercode, for example as a netlist, code for configuring a programmablechip, as a hardware description language defining an integrated circuitat any level, including as register transfer level (RTL) code, ashigh-level circuit representations such as Verilog or VHDL, and aslow-level circuit representations such as OASIS® and GDSII. Higher levelrepresentations which logically define an integrated circuit (such asRTL) may be processed at a computer system configured for generating amanufacturing definition of an integrated circuit in the context of asoftware environment comprising definitions of circuit elements andrules for combining those elements in order to generate themanufacturing definition of an integrated circuit so defined by therepresentation. As is typically the case with software executing at acomputer system so as to define a machine, one or more intermediate usersteps (e.g. providing commands, variables etc.) may be required in orderfor a computer system configured for generating a manufacturingdefinition of an integrated circuit to execute code defining anintegrated circuit so as to generate the manufacturing definition ofthat integrated circuit.

An example of processing an integrated circuit definition dataset at anintegrated circuit manufacturing system so as to configure the system tomanufacture a data processing system will now be described with respectto FIG. 6.

FIG. 6 shows an example of an integrated circuit (IC) manufacturingsystem 1002 which is configured to manufacture a data processing systemas described in any of the examples herein. In particular, the ICmanufacturing system 1002 comprises a layout processing system 1004 andan integrated circuit generation system 1006. The IC manufacturingsystem 1002 is configured to receive an IC definition dataset (e.g.defining a data processing system as described in any of the examplesherein), process the IC definition dataset, and generate an IC accordingto the IC definition dataset (e.g. which embodies a data processingsystem as described in any of the examples herein). The processing ofthe IC definition dataset configures the IC manufacturing system 1002 tomanufacture an integrated circuit embodying a data processing system asdescribed in any of the examples herein.

The layout processing system 1004 is configured to receive and processthe IC definition dataset to determine a circuit layout. Methods ofdetermining a circuit layout from an IC definition dataset are known inthe art, and for example may involve synthesising RTL code to determinea gate level representation of a circuit to be generated, e.g. in termsof logical components (e.g. NAND, NOR, AND, OR, MUX and FLIP-FLOPcomponents). A circuit layout can be determined from the gate levelrepresentation of the circuit by determining positional information forthe logical components. This may be done automatically or with userinvolvement in order to optimise the circuit layout. When the layoutprocessing system 1004 has determined the circuit layout it may output acircuit layout definition to the IC generation system 1006. A circuitlayout definition may be, for example, a circuit layout description.

The IC generation system 1006 generates an IC according to the circuitlayout definition, as is known in the art. For example, the ICgeneration system 1006 may implement a semiconductor device fabricationprocess to generate the IC, which may involve a multiple-step sequenceof photo lithographic and chemical processing steps during whichelectronic circuits are gradually created on a wafer made ofsemiconducting material. The circuit layout definition may be in theform of a mask which can be used in a lithographic process forgenerating an IC according to the circuit definition. Alternatively, thecircuit layout definition provided to the IC generation system 1006 maybe in the form of computer-readable code which the IC generation system1006 can use to form a suitable mask for use in generating an IC.

The different processes performed by the IC manufacturing system 1002may be implemented all in one location, e.g. by one party.Alternatively, the IC manufacturing system 1002 may be a distributedsystem such that some of the processes may be performed at differentlocations, and may be performed by different parties. For example, someof the stages of: (i) synthesising RTL code representing the ICdefinition dataset to form a gate level representation of a circuit tobe generated, (ii) generating a circuit layout based on the gate levelrepresentation, (iii) forming a mask in accordance with the circuitlayout, and (iv) fabricating an integrated circuit using the mask, maybe performed in different locations and/or by different parties.

In other examples, processing of the integrated circuit definitiondataset at an integrated circuit manufacturing system may configure thesystem to manufacture a data processing system without the IC definitiondataset being processed so as to determine a circuit layout. Forinstance, an integrated circuit definition dataset may define theconfiguration of a reconfigurable processor, such as an FPGA, and theprocessing of that dataset may configure an IC manufacturing system togenerate a reconfigurable processor having that defined configuration(e.g. by loading configuration data to the FPGA).

In some embodiments, an integrated circuit manufacturing definitiondataset, when processed in an integrated circuit manufacturing system,may cause an integrated circuit manufacturing system to generate adevice as described herein. For example, the configuration of anintegrated circuit manufacturing system in the manner described abovewith respect to FIG. 6 by an integrated circuit manufacturing definitiondataset may cause a device as described herein to be manufactured.

In some examples, an integrated circuit definition dataset could includesoftware which runs on hardware defined at the dataset or in combinationwith hardware defined at the dataset. In the example shown in FIG. 6,the IC generation system may further be configured by an integratedcircuit definition dataset to, on manufacturing an integrated circuit,load firmware onto that integrated circuit in accordance with programcode defined at the integrated circuit definition dataset or otherwiseprovide program code with the integrated circuit for use with theintegrated circuit.

The implementation of concepts set forth in this application in devices,apparatus, modules, and/or systems (as well as in methods implementedherein) may give rise to performance improvements when compared withknown implementations. The performance improvements may include one ormore of increased computational performance, reduced latency, increasedthroughput, and/or reduced power consumption. During manufacture of suchdevices, apparatus, modules, and systems (e.g. in integrated circuits)performance improvements can be traded-off against the physicalimplementation, thereby improving the method of manufacture. Forexample, a performance improvement may be traded against layout area,thereby matching the performance of a known implementation but usingless silicon. This may be done, for example, by reusing functionalblocks in a serialised fashion or sharing functional blocks betweenelements of the devices, apparatus, modules and/or systems. Conversely,concepts set forth in this application that give rise to improvements inthe physical implementation of the devices, apparatus, modules, andsystems (such as reduced silicon area) may be traded for improvedperformance. This may be done, for example, by manufacturing multipleinstances of a module within a predefined area budget.

The implementation of concepts set forth in this application in devices,apparatus, modules, and/or systems (as well as in methods implementedherein) may give rise to performance improvements when compared withknown implementations. The performance improvements may include one ormore of increased computational performance, reduced latency, increasedthroughput, and/or reduced power consumption. During manufacture of suchdevices, apparatus, modules, and systems (e.g. in integrated circuits)performance improvements can be traded-off against the physicalimplementation, thereby improving the method of manufacture. Forexample, a performance improvement may be traded against layout area,thereby matching the performance of a known implementation but usingless silicon. This may be done, for example, by reusing functionalblocks in a serialised fashion or sharing functional blocks betweenelements of the devices, apparatus, modules and/or systems. Conversely,concepts set forth in this application that give rise to improvements inthe physical implementation of the devices, apparatus, modules, andsystems (such as reduced silicon area) may be traded for improvedperformance. This may be done, for example, by manufacturing multipleinstances of a module within a predefined area budget.

The applicant hereby discloses in isolation each individual featuredescribed herein and any combination of two or more such features, tothe extent that such features or combinations are capable of beingcarried out based on the present specification as a whole in the lightof the common general knowledge of a person skilled in the art,irrespective of whether such features or combinations of features solveany problems disclosed herein. In view of the foregoing description itwill be evident to a person skilled in the art that variousmodifications may be made within the scope of the invention.

What is claimed is:
 1. A method of filtering a target pixel in an image,comprising: forming, for a kernel of pixels comprising the target pixeland its neighbouring pixels, a data model to model pixel values withinthe kernel; calculating a weight for each pixel of the kernelcomprising: (i) a geometric term dependent on a difference in positionbetween that pixel and the target pixel; and (ii) a data term dependenton a difference between a pixel value of that pixel and its predictedpixel value according to the data model; and using the calculatedweights for the pixels in the kernel to form a filtered pixel value forthe target pixel.
 2. The method of claim 1, wherein said using thecalculated weights comprises: updating the data model with a weightedregression analysis technique using the calculated weights for thepixels of the kernel; and evaluating the updated data model at thetarget pixel position so as to form the filtered pixel value for thetarget pixel.
 3. The method of claim 2, the method further comprisingperforming one or more iterations of the calculating and updating steps,wherein updated weights are calculated using the updated data model ofthe preceding iteration.
 4. The method of claim 2, wherein updating thedata model comprises minimising a weighted sum of the squared residualerrors between the pixel values of the kernel predicted by the datamodel and the corresponding actual pixel values of the kernel.
 5. Themethod of claim 2, wherein the weighted regression analysis techniquecomprises performing a weighted least squares method.
 6. The method ofclaim 2, wherein the weighted regression analysis technique comprisesperforming a weighted local gradient measurements method.
 7. The methodof claim 1, wherein said forming a data model comprises applying a firstfilter to the kernel so as to form a target pixel value for use incalculating the weights.
 8. The method of claim 7, wherein the firstfilter is a bilateral filter.
 9. The method of claim 1, wherein the datamodel is defined by one or more parameters including one or moregradient parameters, β, and an estimated value, Î, at the position ofthe target pixel, and wherein forming the data model comprises selectinga data model defining a curve or surface suitable for modelling thepixel values within the kernel, and setting the one or more gradientparameters of the data model to zero.
 10. The method of claim 1, whereinthe data model is a bilinear data model, a linear data model, abiquadratic data model, a quadratic data model, a parametric data modelor a polynomial data model.
 11. The method of claim 1, wherein eachpixel value comprises one or more characteristics of the respectivepixel.
 12. The method of claim 11, wherein each characteristic is one ormore of depth information, information describing normal vectors forsurfaces identified in the image, texture information, luma, luminance,chrominance, brightness, lightness, hue, saturation, chroma,colourfulness, or any colour component.
 13. The method of claim 1,wherein the filtered pixel value for the target pixel is formed for afirst channel, the method further comprising: forming a second filteredpixel value for the target pixel for a second channel in dependence on asecond data model, by forming, for the kernel of pixels comprising thetarget pixel and its neighbouring pixels, a second data model to model asecond characteristic represented by pixel values within the kernel;calculating a weight for each pixel of the kernel comprising: (i) ageometric term dependent on a difference in position between that pixeland the target pixel; and (ii) a data term dependent on a differencebetween a pixel value of that pixel and its predicted pixel valueaccording to the second data model; and using the calculated weights forthe pixels in the kernel so as to form a second filtered pixel value forthe target pixel.
 14. The method of claim 1, wherein the kernel issymmetric about the target pixel.
 15. The method of claim 1, wherein thekernel is asymmetric about the target pixel.
 16. The method of claim 1,wherein the filtering is cross filtering, such that the filtered pixelvalue is in a first channel, and the data term is dependent on pixelvalue differences in a second channel.
 17. The method of claim 16,wherein the data term is dependent on pixel value differences in morethan one channel.
 18. The method of claim 1, wherein said forming a datamodel comprises: determining average gradients (β) in both x and ydirections, from a summation of multiple pixel value differencesdetermined from pairs of pixels located within the kernel; determining,from each pixel in the kernel, an estimated pixel value Î at the targetpixel position based on the determined average gradients; anddetermining a model pixel value Î at the target pixel position byperforming a weighted sum of the estimated pixel values Î determinedfrom each of the pixels in the kernel.
 19. A data processing system forfiltering a target pixel in an image, the data processing systemcomprising: data model formation logic configured to form, for a kernelof pixels comprising the target pixel and its neighbouring pixels, adata model to model pixel values within the kernel; weight calculatinglogic configured to calculate a weight for each pixel of the kernelcomprising: (i) a geometric term dependent on a difference in positionbetween that pixel and the target pixel; and (ii) a data term dependenton a difference between a pixel value of that pixel and its predictedpixel value according to the data model; and data modelling logicconfigured to use the calculated weights for the pixels in the kernel soas to form a filtered pixel value for the target pixel.
 20. Anon-transitory computer readable storage medium having stored thereoncomputer readable instructions that, when executed at a computer system,cause the computer system to: form, for a kernel of pixels comprising atarget pixel in an image and its neighbouring pixels, a data model tomodel pixel values within the kernel; calculate a weight for each pixelof the kernel comprising: (i) a geometric term dependent on a differencein position between that pixel and the target pixel; and (ii) a dataterm dependent on a difference between a pixel value of that pixel andits predicted pixel value according to the data model; and use thecalculated weights for the pixels in the kernel to form a filtered pixelvalue for the target pixel.